1 Loading Libraries

#install.packages("apaTables")
#install.packages("kableExtra")

library(psych) # for the describe() command and the corr.test() command
library(apaTables) # to create our correlation table
library(kableExtra) # to create our correlation table

2 Importing Data

d <- read.csv(file="Data/projectdata.csv", header=T)

# For HW, import the your project dataset you cleaned previously; this will be the dataset you'll use throughout the rest of the semester

3 State Your Hypothesis

There will be a significant relationship between perceived stress, perceived social support, and general self-efficacy. Specifically, perceived stress will be negatively related to perceived social support and negatively related to general self-efficacy, and perceived social support will be positively related to general self-efficacy.

4 Check Your Variables

# you only need to check the variables you're using in the current analysis
# it's always a good idea to look them to be sure that everything is correct
str(d)
## 'data.frame':    3146 obs. of  7 variables:
##  $ ResponseID: chr  "R_BJN3bQqi1zUMid3" "R_2TGbiBXmAtxywsD" "R_12G7bIqN2wB2N65" "R_39pldNoon8CePfP" ...
##  $ income    : chr  "1 low" "1 low" "rather not say" "rather not say" ...
##  $ edu       : chr  "2 Currently in college" "5 Completed Bachelors Degree" "2 Currently in college" "2 Currently in college" ...
##  $ idea      : num  3.75 3.88 3.75 3.75 3.5 ...
##  $ swb       : num  4.33 4.17 1.83 5.17 3.67 ...
##  $ efficacy  : num  3.4 3.4 2.2 2.8 3 2.4 2.3 3 3 3.7 ...
##  $ stress    : num  3.3 3.3 4 3.2 3.1 3.5 3.3 2.4 2.9 2.7 ...
# Since we're focusing only on our continuous variables, we're going to subset them into their own dataframe. This will make some stuff we're doing later on easier.

d2 <- subset(d, select=c(stress, swb, efficacy))

# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)

describe(d2)
##          vars    n mean   sd median trimmed  mad min max range  skew kurtosis
## stress      1 3146 3.05 0.60   3.00    3.05 0.59 1.3 4.7   3.4  0.03    -0.16
## swb         2 3146 4.47 1.32   4.67    4.53 1.48 1.0 7.0   6.0 -0.36    -0.45
## efficacy    3 3146 3.13 0.45   3.10    3.13 0.44 1.1 4.0   2.9 -0.24     0.45
##            se
## stress   0.01
## swb      0.02
## efficacy 0.01
# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.


# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.

hist(d2$stress)

hist(d2$swb)

hist(d2$efficacy)

# last, use scatterplots to examine your continuous variables together, for each pairing
# because we are looking at 3 variables, we will have 3 pairings/plots. 

plot(d2$stress, d2$swb)

plot(d2$stress, d2$efficacy)

plot(d2$swb, d2$efficacy)

5 Check Your Assumptions

5.1 Pearson’s Correlation Coefficient Assumptions

  • Should have two measurements for each participant.
  • Variables should be continuous and normally distributed.
  • Outliers should be identified and removed.
  • Relationship between the variables should be linear.

5.1.1 Checking for Outliers

Note: For correlations, you will NOT screen out outliers or take any action based on what you see here. This is something you will simply check and then discuss in your write-up.We will learn how to removed outliers in later analyses.

# We are going to standardize (z-score) all of our 3 variables, and check them for outliers.

d2$stress <- scale(d2$stress, center=T, scale=T)
hist(d2$stress)

sum(d2$stress < -3 | d2$stress > 3)
## [1] 0
d2$swb <- scale(d2$swb, center=T, scale=T)
hist(d2$swb)

sum(d2$swb < -3 | d2$swb > 3)
## [1] 0
d2$efficacy <- scale(d2$efficacy, center=T, scale=T)
hist(d2$efficacy)

sum(d2$efficacy < -3 | d2$efficacy > 3)
## [1] 15

5.2 Issues with My Data

Two of my variables meet all of the assumptions of Pearson’s correlation coefficient. All three variables were normally distributed according to their skewness and kurtosis values. Stress (skew = 0.03, kurtosis = -0.16), social support (skew = -0.36, kurtosis = -0.45), and self-efficacy (skew = -0.24, kurtosis = 0.45) all fell within acceptable ranges. Stress and well-being did not have any outliers while self-efficacy has 15 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction. Overall, the assumptions were reasonably met, though correlations involving self-efficacy should be interpreted with slight caution due to the presence of outliers.

6 Run a Single Correlation

corr_output <- corr.test(d2$stress, d2$swb)

7 View Single Correlation

corr_output
## Call:corr.test(x = d2$stress, y = d2$swb)
## Correlation matrix 
##      [,1]
## [1,] -0.5
## Sample Size 
## [1] 3146
## These are the unadjusted probability values.
##   The probability values  adjusted for multiple tests are in the p.adj object. 
##      [,1]
## [1,]    0
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

8 Create a Correlation Matrix

corr_output_m <- corr.test(d2)

9 View Test Output

corr_output_m
## Call:corr.test(x = d2)
## Correlation matrix 
##          stress  swb efficacy
## stress      1.0 -0.5     -0.4
## swb        -0.5  1.0      0.4
## efficacy   -0.4  0.4      1.0
## Sample Size 
## [1] 3146
## Probability values (Entries above the diagonal are adjusted for multiple tests.) 
##          stress swb efficacy
## stress        0   0        0
## swb           0   0        0
## efficacy      0   0        0
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option
# Remember to report the p-values from the matrix that are ABOVE the diagonal!

Remember, Pearson’s r is also an effect size! We don’t report effect sizes for non-sig correlations.

  • Strong: Between |0.50| and |1|
  • Moderate: Between |0.30| and |0.49|
  • Weak: Between |0.10| and |0.29|
  • Trivial: Less than |0.09|

10 Write Up Results

To test our hypothesis that stress, self efficacy, and social support would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All three of the variables (stress, self efficacy, and social support) met the required assumptions of the test, with both meeting the standards of normality. Stress and subjective well-being contained no outliers, while self-efficacy included a small number of outliers (n = 15), meaning it did not fully meet all assumptions. Given the large sample size, these outliers were unlikely to substantially impact the results.

As predicted, we found that all three varibales were significantly correlated (all ps < .001). The effect sizes of all correlations were large (rs > .50; Cohen, 1988). Additionally, unhappiness was found to be negatively related to life satisfaction, and positively related to fakeness, as predicted. Please refer to the correlation coefficients reported in Table 1.

Stress was negatively correlated with social support (r = −.50, p < .001) and negatively correlated with self-efficacy (r = −.40, p < .001). Also social support was positively correlated with self-efficacy (r = .40, p < .001). The relationship between stress and social support was large while the relationships involving self-efficacy were moderate. All findings supported the original hypotheses. Please refer to the correlation coefficients reported in Table 1.

Table 1: Means, standard deviations, and correlations with confidence intervals
Variable M SD 1 2
Stress 3.05 0.60
Social Support 4.47 1.32 -.50**
[-.53, -.48]
Self Efficacy 3.13 0.45 -.40** .40**
[-.43, -.38] [.37, .43]
Note:
M and SD are used to represent mean and standard deviation, respectively. Values in square brackets indicate the 95% confidence interval. The confidence interval is a plausible range of population correlations that could have caused the sample correlation.
* indicates p < .05
** indicates p < .01.

References

Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.